Expression of type ExprTuple

from the theory of proveit.core_expr_types.operations

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, f, g, n
from proveit.core_expr_types import f__x_1_to_n, g__x_1_to_n, x_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [f, g, x_1_to_n], instance_expr = Equals(f__x_1_to_n, g__x_1_to_n), condition = Equals(f, g)), InSet(n, Natural))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(n \mapsto \left\{\forall_{f, g, x_{1}, x_{2}, \ldots, x_{n}~|~f = g}~\left(f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = g\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right) \textrm{ if } n \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 27 body: 3
2	ExprTuple	27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	27, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	21, 22, 24
13	Conditional	value: 14 condition: 15
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 21 operands: 23
20	Operation	operator: 22 operands: 23
21	Variable
22	Variable
23	ExprTuple	24
24	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
25	Lambda	parameter: 31 body: 28
26	Literal
27	Variable
28	IndexedVar	variable: 29 index: 31
29	Variable
30	ExprTuple	31
31	Variable